you can check it yourself using The Remainder Theorem
I did not know where to put this topic.
I am working doing long division on polynomials.
I had
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(x-2)|x^4-3x^2+4x-9
I ended up with a remainder of -5. I was just wondering if someone could confirm if this is correct or not, because I can not tell if I have done it correct or not.
EDIT: Actually I think I did do it wrong.....I got 3 as a remainder this time.
you can check it yourself using The Remainder Theorem
Yes, 3 is correct.
x divides into x^4, x^3 times. x^3(x- 2)= x^4- 2x^3. x^4- 0x^3- 3x^2+ 4x- 9- (x^4- 2x^3)= 2x^3- 3x^2+ 4x- 9.
x divides into 2x^3, 2x^2 times. 2x^2(x- 2)= 2x^3- 4x^2. 2x^3- 3x^2+ 4x- 9- (2x^3- 4x^2)= x^2+ 4x- 9.
x divides into x^2, x times. x(x- 2)= x^2- 2x. x^2+ 4x- 9- (x^2- 2x)= 6x- 9.
x divides into 6x, 6 times. 6(x- 2)= 6x- 12. 6x- 9- (6x- 12)= 3.